Question 1

Write the exponential equation in logarithmic form.​ $2 ^ { 3 } = 8$ ​

Accepted Answer

A)  $\log _ { 8 } 2 = 3$ 
B)  $\log _ { 2 } 8 = 3$ 
C)  $\log _ { 8 } 2 = - 3$ 
D)  $\log _ { 2 } 3 = 8$ 
E)  $\log _ { 2 } 8 = \frac { 1 } { 3 }$ 
A)  $\log _ { 8 } 2 = 3$ 
B)  $\log _ { 2 } 8 = 3$ 
C)  $\log _ { 8 } 2 = - 3$ 
D)  $\log _ { 2 } 3 = 8$ 
E)  $\log _ { 2 } 8 = \frac { 1 } { 3 }$

Question 2

Evaluate $f ( x ) = \log x$ at the indicated value of x.Round your result to three decimal places.​ $x = \frac { 1 } { 100 }$ ​

Accepted Answer

A) -0.5 
B) 0.01 
C) 0.5 
D) -2 
E) 2 
A) -0.5 
B) 0.01 
C) 0.5 
D) -2 
E) 2

Question 3

Identify the value of the function $f ( x ) = \log _ { 10 } x$ at $x = 315$ .Round to 3 decimal places.

Accepted Answer

A) 2.498 
B) 2.998 
C) 3.498 
D) 3.998 
E) 5.753 
A) 2.498 
B) 2.998 
C) 3.498 
D) 3.998 
E) 5.753

Question 4

Write the exponential equation in logarithmic form.​ $24 ^ { 2 } = 576$ ​

Accepted Answer

A)  $\log _ { 24 } 576 = 2$ 
B)  $\log _ { 24 } 576 = \frac { 1 } { 2 }$ 
C)  $\log _ { 576 } 24 = 2$ 
D)  $\log _ { 24 } 576 = - 2$ 
E)  $\log _ { 24 } 2 = 576$ 
A)  $\log _ { 24 } 576 = 2$ 
B)  $\log _ { 24 } 576 = \frac { 1 } { 2 }$ 
C)  $\log _ { 576 } 24 = 2$ 
D)  $\log _ { 24 } 576 = - 2$ 
E)  $\log _ { 24 } 2 = 576$

Question 5

Evaluate the function at the indicated value of $x = b ^ { - 7 }$ .​ $g ( x ) = \log _ { b } x$ ​

Accepted Answer

A) 7 
B) 0 
C)  $\frac { 1 } { 7 }$ 
D) -7 
E)  $- \frac { 1 } { 7 }$ 
A) 7 
B) 0 
C)  $\frac { 1 } { 7 }$ 
D) -7 
E)  $- \frac { 1 } { 7 }$

Question 6

Find the value of b,if any,that would cause the graph of $y = \log _ { b } x$ to look like the graph shown.​   ​

Accepted Answer

A) b = 3.5 
B) b = 4.5 
C) b = 2 
D) b = 4 
E) b = 1 
A) b = 3.5 
B) b = 4.5 
C) b = 2 
D) b = 4 
E) b = 1

Question 7

Write the exponential equation in logarithmic form.​ $10 ^ { - 3 } = 0.00100$ ​

Accepted Answer

A)  $\log 3 = 0.00100$ 
B)  $\log 0.00100 = - \frac { 1 } { 3 }$ 
C)  $\log 0.00100 = - 3$ 
D)  $\log 0.00100 = \frac { 1 } { 3 }$ 
E)  $\log 0.00100 = 3$ 
A)  $\log 3 = 0.00100$ 
B)  $\log 0.00100 = - \frac { 1 } { 3 }$ 
C)  $\log 0.00100 = - 3$ 
D)  $\log 0.00100 = \frac { 1 } { 3 }$ 
E)  $\log 0.00100 = 3$

Question 8

Evaluate $g ( x ) = \ln x$ at the indicated value of x.​ $x = e ^ { 7 }$ ​

Accepted Answer

A)  $- \frac { 1 } { 7 }$ 
B)  $e ^ { 2 }$ 
C) -7 
D) 7 
E)  $\frac { 1 } { 7 }$ 
A)  $- \frac { 1 } { 7 }$ 
B)  $e ^ { 2 }$ 
C) -7 
D) 7 
E)  $\frac { 1 } { 7 }$

Question 9

Write the equation $6 ^ { 5 } = 7,776$ in logarithmic form. ​

Accepted Answer

A)  $\log _ { 6 } 7,776 = 5$ 
B)  $\log _ { 5 } 6 = 7,776$ 
C)  $\log _ { 7,776 } 6 = 5$ 
D)  $\log _ { 6 } 5 = 7,776$ 
E)  $\log _ { 5 } 7,776 = 6$ 
A)  $\log _ { 6 } 7,776 = 5$ 
B)  $\log _ { 5 } 6 = 7,776$ 
C)  $\log _ { 7,776 } 6 = 5$ 
D)  $\log _ { 6 } 5 = 7,776$ 
E)  $\log _ { 5 } 7,776 = 6$

Question 10

Evaluate the function at the indicated value of $x = 23.92$ .Round your result to three decimal places.​ $f ( x ) = \ln x$ ​

Accepted Answer

A) 3.175 
B) -2.076 
C) -3.175 
D) 2.076 
E) 23.92 
A) 3.175 
B) -2.076 
C) -3.175 
D) 2.076 
E) 23.92

Question 11

Evaluate the function $f ( x ) = \log _ { 2 } x$ at $x = \frac { 1 } { 2 }$ without using a calculator.

Accepted Answer

A) 0 
B) -1 
C) -2 
D) 2 
E)  $$\frac { 1 } { 2 }$$ 
A) 0 
B) -1 
C) -2 
D) 2 
E)  $$\frac { 1 } { 2 }$$

Question 12

Evaluate $f ( x ) = \log x$ at the indicated value of x.Round your result to three decimal places.​ $x = 70.75$ ​

Accepted Answer

A) 1.85 
B) 0.541 
C) 0.014 
D) -0.541 
E) -1.85 
A) 1.85 
B) 0.541 
C) 0.014 
D) -0.541 
E) -1.85

Question 13

Identify the x-intercept of the function $f ( x ) = 4 \ln ( x - 1 )$ .

Accepted Answer

A)  $x = 1$ 
B)  $x = 0$ 
C)  $x = 4$ 
D)  $x = 2$ 
E) The function has no x-intercept. 
A)  $x = 1$ 
B)  $x = 0$ 
C)  $x = 4$ 
D)  $x = 2$ 
E) The function has no x-intercept.

Question 14

Identify the value of the function $f ( x ) = \log _ { 10 } x$ at $x = 915$ .Round to 3 decimal places.

Accepted Answer

A) 6.819 
B) 3.961 
C) 2.961 
D) 4.461 
E) 3.461 
A) 6.819 
B) 3.961 
C) 2.961 
D) 4.461 
E) 3.461

Question 15

Use a calculator to find the value for $\log 0.85759$ to four decimal places. ​

Accepted Answer

A) -0.0667 
B) -0.1536 
C) 0.9333 
D) -0.9333 
E) 0.0667 
A) -0.0667 
B) -0.1536 
C) 0.9333 
D) -0.9333 
E) 0.0667

Question 16

Write the logarithmic equation $\ln 4 = 1.386 \ldots$ in exponential form.

Accepted Answer

A)  $e ^ { 1.386 \cdots } = 4$ 
B)  $e ^ { 4 } = 1.386 \ldots$ 
C)  $2.303 e ^ { 1.386 \cdots } = 4$ 
D)  $10 ^ { 4 } = 1.386 \ldots$ 
E)  $2.303 \times 10 ^ { 4 } = 1.386 \ldots$ 
A)  $e ^ { 1.386 \cdots } = 4$ 
B)  $e ^ { 4 } = 1.386 \ldots$ 
C)  $2.303 e ^ { 1.386 \cdots } = 4$ 
D)  $10 ^ { 4 } = 1.386 \ldots$ 
E)  $2.303 \times 10 ^ { 4 } = 1.386 \ldots$

Question 17

Use a calculator to find a value for $\ln ( 30.9 )$ to four decimal places. ​

Accepted Answer

A) -3.4308 
B) 3.4308 
C) -1.49 
D) 1.49 
E) 5.7333 
A) -3.4308 
B) 3.4308 
C) -1.49 
D) 1.49 
E) 5.7333

Question 18

Evaluate $g ( x ) = \ln x$ at the indicated value of x.​ $x = e ^ { - 9 }$ ​

Accepted Answer

A) 9 
B)  $- \frac { 1 } { 9 }$ 
C) -9 
D)  $\frac { 1 } { 9 }$ 
E)  $e ^ { - 9 }$ 
A) 9 
B)  $- \frac { 1 } { 9 }$ 
C) -9 
D)  $\frac { 1 } { 9 }$ 
E)  $e ^ { - 9 }$

Question 19

Rewrite the exponential equation $4 ^ { - 2 } = \frac { 1 } { 16 }$ in logarithmic form.

Accepted Answer

A)  $\log _ { 4 } \frac { 1 } { 16 } = - 2$ 
B)  $\log _ { 2 } 16 = - 2$ 
C)  $\log _ { 4 } 16 = - 2$ 
D)  $\log _ { 16 } 4 = - 2$ 
E)  $$\log _ { 4 } \frac { 1 } { 16 } = 2$$ 
A)  $\log _ { 4 } \frac { 1 } { 16 } = - 2$ 
B)  $\log _ { 2 } 16 = - 2$ 
C)  $\log _ { 4 } 16 = - 2$ 
D)  $\log _ { 16 } 4 = - 2$ 
E)  $$\log _ { 4 } \frac { 1 } { 16 } = 2$$

Question 20

Write the logarithmic equation in exponential form.​ $\log _ { 7 } 343 = 3$ ​

Accepted Answer

A)  $7 ^ { 343 } = 2$ 
B)  $7 ^ { 3 } = 77$ 
C)  $7 ^ { 3 } = 343$ 
D)  $7 ^ { 3 } = 14$ 
E)  $343 ^ { 7 } = 2$ 
A)  $7 ^ { 343 } = 2$ 
B)  $7 ^ { 3 } = 77$ 
C)  $7 ^ { 3 } = 343$ 
D)  $7 ^ { 3 } = 14$ 
E)  $343 ^ { 7 } = 2$

Exam 19: Logarithmic Functions and Their Graphs

Write the exponential equation in logarithmic form.​ 23=82 ^ { 3 } = 823=8 ​

Evaluate f(x)=log⁡xf ( x ) = \log xf(x)=logx at the indicated value of x.Round your result to three decimal places.​ x=1100x = \frac { 1 } { 100 }x=1001​ ​

Identify the value of the function f(x)=log⁡10xf ( x ) = \log _ { 10 } xf(x)=log10​x at x=315x = 315x=315 .Round to 3 decimal places.

Write the exponential equation in logarithmic form.​ 242=57624 ^ { 2 } = 576242=576 ​

Evaluate the function at the indicated value of x=b−7x = b ^ { - 7 }x=b−7 .​ g(x)=log⁡bxg ( x ) = \log _ { b } xg(x)=logb​x ​

Find the value of b,if any,that would cause the graph of y=log⁡bxy = \log _ { b } xy=logb​x to look like the graph shown.​ ​

Write the exponential equation in logarithmic form.​ 10−3=0.0010010 ^ { - 3 } = 0.0010010−3=0.00100 ​

Evaluate g(x)=ln⁡xg ( x ) = \ln xg(x)=lnx at the indicated value of x.​ x=e7x = e ^ { 7 }x=e7 ​

Write the equation 65=7,7766 ^ { 5 } = 7,77665=7,776 in logarithmic form. ​

Evaluate the function at the indicated value of x=23.92x = 23.92x=23.92 .Round your result to three decimal places.​ f(x)=ln⁡xf ( x ) = \ln xf(x)=lnx ​

Evaluate the function f(x)=log⁡2xf ( x ) = \log _ { 2 } xf(x)=log2​x at x=12x = \frac { 1 } { 2 }x=21​ without using a calculator.

Evaluate f(x)=log⁡xf ( x ) = \log xf(x)=logx at the indicated value of x.Round your result to three decimal places.​ x=70.75x = 70.75x=70.75 ​

Identify the x-intercept of the function f(x)=4ln⁡(x−1)f ( x ) = 4 \ln ( x - 1 )f(x)=4ln(x−1) .

Identify the value of the function f(x)=log⁡10xf ( x ) = \log _ { 10 } xf(x)=log10​x at x=915x = 915x=915 .Round to 3 decimal places.

Use a calculator to find the value for log⁡0.85759\log 0.85759log0.85759 to four decimal places. ​

Write the logarithmic equation ln⁡4=1.386…\ln 4 = 1.386 \ldotsln4=1.386… in exponential form.

Use a calculator to find a value for ln⁡(30.9)\ln ( 30.9 )ln(30.9) to four decimal places. ​

Evaluate g(x)=ln⁡xg ( x ) = \ln xg(x)=lnx at the indicated value of x.​ x=e−9x = e ^ { - 9 }x=e−9 ​

Rewrite the exponential equation 4−2=1164 ^ { - 2 } = \frac { 1 } { 16 }4−2=161​ in logarithmic form.

Write the logarithmic equation in exponential form.​ log⁡7343=3\log _ { 7 } 343 = 3log7​343=3 ​

Rectangular Coordinates

Graphs of Equations

Linear Equations in Two Variables

Functions

Analyzing Graphs of Functions

A Library of Parent Functions

Transformations of Functions

Combinations of Functions Composite Functions

Inverse Functions

Mathematical Modeling and Variation

Quadratic Functions and Models

Polynomial Functions of Higher Degree

Polynomial and Synthetic Division

Complex Numbers

Zeros of Polynomial Functions

Rational Functions

Nonlinear Inequalities

Exponential Functions and Their Graphs

Properties of Logarithms

Exponential and Logarithmic Equations

Exponential and Logarithmic Models

Radian and Degree Measure

Trigonometric Functions The Unit Circle

Right Triangle Trigonometry

Trigonometric Functions of Any Angle

Graphs of Sine and Cosine Functions

Graphs of Other Trigonometric Functions

Inverse Trigonometric Functions

Applications and Models

Using Fundamental Identities

Verifying Trigonometric Equations

Solving Trigonometric Equations

Sum and Difference Formulas

Multiple Angle and Product to Sum Formulas

Law of Sines

Law of Cosines

Vectors in the Plane

Vectors and Dot Products

Trigonometric Form of a Complex Number

Linear and Nonlinear Systems of Equations

Two Variable Linear Systems

Multivariable Linear Systems

Partial Fractions

Systems of Inequalities

Linear Programming

Matrices and Systems of Equations

Operations With Matrices

The Inverse of a Square Matrix

The Determinant of a Square Matrix

Applications of Matrices and Determinants

Sequences and Series

Arithmetic Sequences and Partial Sums

Geometric Sequences and Series

Mathematical Induction

The Binomial Theorem

Counting Principles

Probability

Lines

Introduction to Conics Parabolas

Write the exponential equation in logarithmic form. $2 ^ { 3 } = 8$

Evaluate $f ( x ) = \log x$ at the indicated value of x.Round your result to three decimal places. $x = \frac { 1 } { 100 }$

Identify the value of the function $f ( x ) = \log _ { 10 } x$ at $x = 315$ .Round to 3 decimal places.

Write the exponential equation in logarithmic form. $24 ^ { 2 } = 576$

Evaluate the function at the indicated value of $x = b ^ { - 7 }$ . $g ( x ) = \log _ { b } x$

Find the value of b,if any,that would cause the graph of $y = \log _ { b } x$ to look like the graph shown. $Find the value of b,if any,that would cause the graph of y = \log _ { b } x to look like the graph shown. $

Write the exponential equation in logarithmic form. $10 ^ { - 3 } = 0.00100$

Evaluate $g ( x ) = \ln x$ at the indicated value of x. $x = e ^ { 7 }$

Write the equation $6 ^ { 5 } = 7,776$ in logarithmic form.

Evaluate the function at the indicated value of $x = 23.92$ .Round your result to three decimal places. $f ( x ) = \ln x$

Evaluate the function $f ( x ) = \log _ { 2 } x$ at $x = \frac { 1 } { 2 }$ without using a calculator.

Evaluate $f ( x ) = \log x$ at the indicated value of x.Round your result to three decimal places. $x = 70.75$

Identify the x-intercept of the function $f ( x ) = 4 \ln ( x - 1 )$ .

Identify the value of the function $f ( x ) = \log _ { 10 } x$ at $x = 915$ .Round to 3 decimal places.

Use a calculator to find the value for $\log 0.85759$ to four decimal places.

Write the logarithmic equation $\ln 4 = 1.386 \ldots$ in exponential form.

Use a calculator to find a value for $\ln ( 30.9 )$ to four decimal places.

Evaluate $g ( x ) = \ln x$ at the indicated value of x. $x = e ^ { - 9 }$

Rewrite the exponential equation $4 ^ { - 2 } = \frac { 1 } { 16 }$ in logarithmic form.

Write the logarithmic equation in exponential form. $\log _ { 7 } 343 = 3$